J Austral Math Soc Ser A 44 pp164--170, 1988.

On Dual Radicals and Ring Elements

B. de la Rosa and R. Wiegandt

(Received 19 June 1986; revised 14 September 1986)

Abstract

If a property P of ring elements satisfies conditions (a)-(d), then the largest homomorphically closed class having no non-zero P-element is a dual radical is the sense of Andrunakievic, and every dual radical can be obtained in this way. Also properties defined by polynomials are considered and as an application we get various characterizations of the Behrens radical.

1980 AMS Subject Classification: 16A21

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Authors

B. de la Rosa: Department of Mathematics, University of the Orange Free State, Bloemfontein 9300, South Africa.
R. Wiegandt: Mathematical Institute of the Hungarian Academy of Sciences, Budapest, V. Reáltanoda u. 13-15, Hungary.

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Last Modified: Wed Feb 19 10:27:48 2003